What is the probability of flipping a coin 8 times and getting heads 2 times?

Question

perl · Answer

lets define Success S as heads , so failure is F

you want 

P( heads 2 times) = SS FF FF FF , and there are other possibilities

hockeychick23 · Answer

ok so should the probability be 1/4 then

perl · Answer

not quite

perl · Answer

Let X = # of heads
P ( X = 2) = 8 C 2  * (1/2)^8

perl · Answer

I get .109375

hockeychick23 · Answer

ok, so is that where the z chart comes in?

perl · Answer

you would use a z chart if the number of trials was very large

perl · Answer

for example if i asked what is probability of getting 8 heads in 1 million flips, a calculator would have a hard time to solve it using the binomial distribution formula

hockeychick23 · Answer

oh ok, so for the smaller numbers like this one i would just leave it as 10.9%

perl · Answer

does the problem say to estimate it with a normal z distribution

hockeychick23 · Answer

no it just asks what is the probability of flipping a coin 8 times and getting heads 2 times

perl · Answer

then we use the direct formula

perl · Answer

so you are right, for small n we just leave it alone

hockeychick23 · Answer

ok so leave it as 10.9%, thanks!